{
  "id": "1310.3960",
  "version": "v2",
  "published": "2013-10-15T08:41:07.000Z",
  "updated": "2014-06-30T14:42:17.000Z",
  "title": "Variations of Stieltjes-Wigert and q-Laguerre polynomials and their recurrence coefficients",
  "authors": [
    "Lies Boelen",
    "Walter Van Assche"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We look at some extensions of the Stieltjes-Wigert weight functions. First we replace the variable x by x^2 in a family of weight functions given by Askey in 1989 and we show that the recurrence coefficients of the corresponding orthogonal polynomials can be expressed in terms of a solution of the q-discrete Painlev\\'e III equation. Next we consider the q-Laguerre or generalized Stieltjes-Wigert weight functions with a quadratic transformation and derive recursive equations for the recurrence coefficients of the orthogonal polynomials. These turn out to be related to the q-discrete Painlev\\'e V equation. Finally we also consider the little q-Laguerre weight with a quadratic transformation and show that the recurrence coefficients of the orthogonal polynomials are again related to q-discrete Painlev\\'e V.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-30T14:42:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "33E17",
      "42C05",
      "65Q30"
    ],
    "keywords": [
      "recurrence coefficients",
      "q-laguerre polynomials",
      "q-discrete painleve",
      "variations",
      "quadratic transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.3960B"
    }
  }
}